Answer:
The answer is C
Step-by-step explanation:
The roots are −1.87938524, 0.34729635, 1.53208888, −1.87938524, 0.34729635, and 1.53208888. That's 6 roots, which is C.
According to the Fundamental Theorem of Algebra, 6 roots exist for the polynomial function.
What is the fundamental Theorem of Algebra?Fundamental Theorem of Algebra states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero.
Given polynomial function
[tex]f(x)=(x^{3}-3x+1 )^{2}[/tex]
It has [tex](x^{3} )^{2}[/tex] term in the given polynomial
The fundamental theorem of algebra guarantees that a polynomial equation has the same number of roots as its degree.
= 3 × 2
= 6
So, 6 roots exist for the polynomial function.
Find out more information about Fundamental Theorem of Algebra here
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C.
Find the value of x3 + 3x²y + 3xy2 + y when x = 3 and y = 4.
涨涨涨涨
Answer:
[tex]x^3 + 3x\²y + 3xy^2 + y[/tex] [tex]=283[/tex]
[tex]When\ x = 3\ and\ y = 4[/tex]
Step-by-step explanation:
Given
[tex]x^3 + 3x\²y + 3xy^2 + y[/tex]
Required
Solve when x = 3 and y = 4
To do this, we simply substitute 3 for x and 4 for y in [tex]x^3 + 3x\²y + 3xy^2 + y[/tex]
[tex]3^3 + 3 * 3^2 * 4 + 3 * 3 * 4^2 + 4[/tex]
[tex]27 + 3 * 9 * 4 + 3 * 3 * 16 + 4[/tex]
[tex]27 + 108 + 144+ 4[/tex]
[tex]283[/tex]
Hence:
[tex]x^3 + 3x\²y + 3xy^2 + y[/tex] [tex]=283[/tex]
[tex]When\ x = 3\ and\ y = 4[/tex]
Ella invested $2,700 in an account paying an interest rate of 5.4% compounded
monthly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $4,020?
Answer:
The account will take 7 years to reach a value of $4,020
Step-by-step explanation:
Compound Interest
When it occurs interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Ella invested P=$2,700 in an account with an interest rate of r=5.4% (0.054) compounded monthly. Since there are 12 months in a year, n=12.
It will be calculated when will the account have a value of A=$4,020. Substituting all the values in the formula:
[tex]{\displaystyle 4,020=2,700\left(1+{\frac {0.054}{12}}\right)^{12t}}[/tex]
Calculating:
[tex]{\displaystyle 4,020=2,700\left(1.0045)^{12t}}[/tex]
Dividing by 2,700:
[tex]{\displaystyle \frac{4,020}{2,700}=\left(1.0045)^{12t}}[/tex]
To solve this equation for t, we need to apply logarithms:
[tex]{\displaystyle \log\frac{4,020}{2,700}=\log\left(1.0045)^{12t}}[/tex]
Applying the logarithm power rule:
[tex]\displaystyle \log\frac{4,020}{2,700}=12t\log 1.0045[/tex]
Dividing by 12log 1.0045:
[tex]\displaystyle t=\frac{\log\frac{4,020}{2,700}}{12\log 1.0045}[/tex]
Calculating:
t= 7.39 years
Rounding to the nearest year, the account will take 7 years to reach a value of $4,020
Answer:
7
Step-by-step explanation:
which table ordered pairs represents a linesr function (-7, 24) (0,2) (7,24) (14, 103)
(-7 -5) (0,1) (7,7) (14,13)
(-7,-5) (0,2) (7,9) (7,2)
(-7,-5) (0,2) (7,3) (14,6)
Answer:
which table ordered pairs represents a linesr function (-7, 24) (0,2) (7,24) (14, 103)
Step-by-step explanation:
is (2,5) a solution to this system of equation
Y=2x+1
2x+2y=15
(2,5)_________________a solution because____________________________
Question 3 please help?!!!!
Answer:
First choice, 21/50
Step-by-step explanation:
16 + 9 + 22 + 26 + 15 + 12 = 100
Out of 100 tries, 16 times landed on 1 and 26 times landed on 4, added together is 42 times it landed on either a 4 or 1 out of 100
42/100, simplify it with 2, 21/50
Mark incorrectly evaluated the expression 4x+12-x to the power of 2 where is x-2. Identify and correct mark’s mistake.
Plsss help mw
Answer:
The value of [tex]4x+12-x^2[/tex] is 16.
Step-by-step explanation:
The given expression is [tex]4x+12-x^2\ at\ x=2[/tex].
Put x = 2 in the above expression as follows :
[tex]4x+12-x^2=4(2)+12-(2)^2\\\\=8+12-4\\\\=16[/tex]
Hence, the final answer is 16.
which is bigger -5/4 or 128%?
Answer:
128%
Step-by-step explanation:
Because -5/4 is a negative, no matter what is in front of the % in the128%, as long as it's a positive, it is bigger than -5/4
A cafeteria starts with 750 fish sticks for lunch. Each meal they serve uses 6 of the fish sticks, At the end of the lunch there are 42 fish sticks left. Let n be the number of meals served in the cafeteria. Set up and solve an equation to find the value of n.
Answer:
The value of N = 118
Step-by-step explanation:
750 = 6n + 42
move all the numbers that don't contain n to the right side
6n = 750 - 42
6n = 708
708 / 6 = 118
n = 118
plug the numbers back in
6 ( 118) = 708
708 = 708
plug the 42 back in
708 + 42 = 750
Carson’s wheelbarrow can hold 345 pounds. If he has 121 pounds of rock in the wheelbarrow, what number of pounds, p, can he put in the wheelbarrow without going over the weight limit?
Answer:
345 in total. If there are already 121 in: 345-121=224 pounds.
Tetsuo has 50 arcade tokens . Each arcade game at RetroRamam coast 4 tokens . How many games can Tetsuo play ? (middle school problem 7th grade )
Answer:
he can play 12 games
Step-by-step explanation:
but he is gonna have some tokens left over.
How can you use graphs to represent and analyze proportional relationships? EXIT TICKET Write an equation of the form y = kx for the relationship shown in the graph.
Answer:
5, 25
Step-by-step explanation:
Isaiah gave $18 to his Friends. He gave 4 to Ricardo, $7 to Jeremiah, and the rest to Fabian. how much money did Fabian get?
Answer:
Fabian got $7.
Step-by-step explanation:
Isaiah gave $18 to his friends--Ricardo got $4, Jeremiah got $7, and Fabian got the rest. This needs a math equation!
4 + 7 + f = 18
where f is the amount of money Fabian got.
4 + 7 + f = 18
(subtract 4 from both sides)
7 + f = 14
(subtract 7 from both sides)
f = 7
It looks like Fabian got $7! Let's check just to make sure.
4 + 7 + f = 18
4 + 7 + (7) = 18
18 = 18
It checks out!
Holly earns $30 for babysitting 5 hours. She earns $28 when she does chores for 4 hours. Which compares the unit rates?
A. The unit rate for babysitting is $2 per hour more than the unit rate for doing chores
B. The unit rate for babysitting is $1 per hour more than the unit rate for doing chores
C. The unit rate for doing chores is $1 per hour more than the unit rate for babysitting
D. The unit rate for doing chores is $2 per hour more than the unit rate for babysitting
PLEASE HELP! DUE SOON!!!!
Answer: yes
Step-by-step explanation:
What type of triangle is formed by joining the points D(7, 3), E(8, 1), and
F(4, -1)?
Answer:
right triangle
tep-by-step explanation:
i just took the test and worked this out
Write the word sentence as an inequality. Then solve the inequality.
A number x divided by 7 is less than −3.
An inequality is
.
The solution of this inequality is
.
Answer:
x/7<-3x<-21Step-by-step explanation:
x/7<-3x<-3x7x<-21Answer:
The inequality x÷7<-3
The solution x<-21
Step-by-step explanation:
Solving- x÷7<-3
x<-3x7
x<-21
Given that y varies directly with x, and y =10, when x=2. What is the value of x when y=7?
What is the slope of this graph? And is it continuous or discrete?
Answer: 45 degree and continuous
Step-by-step explanation: i used a protractor
disclamer:pls dont sue me i dont think im right
Mr. Ortiz has 3/4 pound of oatmeal.
He uses 2/3 of the oatmeal to bake muffins.
How much oatmeal does Mr. Ortiz have left?
(With Explanation Pls)
Answer:
[tex]\frac{1}{4}\ pound[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\Amount\ of\ oatmeal\ Mr.Ortiz\ has=\frac{3}{4}\ pounds \\Amount\ of\ Oatmeal\ he\ uses\ to\ bake\ muffins=\frac{2}{3}\ of\ the\ amount\ he\ had\\Now,\\Lets\ first\ find\ the\ amount\ of\ oatmeal\ he\ used=\frac{3}{4}*\frac{2}{3}=\frac{1}{2}\ pounds\\Hence,\\The\ amount\ of\ oatmeal\ remains=Total\ amount\ of\ oatmeal-Amount\\ he\ used\ to\ make\ muffins\\Hence,\\The\ amount\ of\ oatmeal\ left\ with\ Mr.\ Ortiz=\frac{3}{4} - \frac{1}{2} =\frac{1}{4}\ pound[/tex]
PLEASE HELPPPPP I NEED IT RIGHT THIS MINUTE PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
The answer is 3
Step-by-step explanation:
1/4(16 + 4)-2 = 3
Hope this helped ya
Answer:
1/4(16+4)-2
1/4(20)-2
5-2
3
Step-by-step explanation:
You need to design a new cereal box for the Yum Yum Cereal Company. The new cereal box must have a volume of 2400 cubic centimeters. Your task is to create a cereal box that would hold a volume of 2400 cubic centimeters of cereal. On your paper, draw the box and label its dimensions. Show your work to verify that the box you drew would hold 2400 cubic centimeters of cereal. Enter in BOTH sets of dimensions here. (Ex: Box #1 - length = ___, width = ____, height = ____, Box #2 - length = ___, width = ____, height = ____)
Answer:
Please find attached the required new cereal boxes for the Yum Yum Cereal Company created with Microsoft Visio
Step-by-step explanation:
The required volume of the cereal box = 2,400 cm³
The box is to be drawn and labeled as follows using Microsoft Visio
Box #1 Length = 16 cm, Width = 15 cm, Height = 10 cm
The volume = Length × Width × Height = 16 cm × 15 cm × 10 cm = 2,400 cm³
Box #2 Length = 30 cm, Width = 10 cm, Height = 8 cm
The volume = Length × Width × Height = 30 cm × 10 cm × 8 cm = 2,400 cm³
In the diagram FEL ~ JOS
Which ratios are equivalent to tan F? Select all that apply. (Don’t just choose one)
9514 1404 393
Answer:
EL/EF and OS/OJ
Step-by-step explanation:
In the similar triangles, angle F and angle J have the same measure, so will have the same tangent. The tangent is the ratio of the opposite side to the adjacent one.
In ΔFEL, the desired ratio is ...
tan(F) = EL/EF . . . . . 2nd choice
In ΔJOS, the equivalent ratio is ...
tan(J) = tan(F) = OS/OJ . . . . . 7th choice
Please help me with 4 (new)
Answer:
First choice, 47/100
Step-by-step explanation:
16 + 9 + 22 + 26 + 15 + 12 = 100
The even numbers are 2, 4, and 6. They rolled two 9 times, four 26 times, and six 12 times. Added together and they're 47, so 47/100
There's no simplification of this fraction as theres no number that can be used to divide both 47 and 100
The function y = -3x + 42 models the average number of dogs at an animal shelter, where x is the number of days after July 1. The function y = 4x + 7 models the average number of cats at the animal shelter, where x is the number of days after July 1. After how many days is the average number of cats and dogs at the shelter the same?
A. 5 days
B. 7 days
C. 35 days
D. 49 days
Answer:
A. 5 days
Step-by-step explanation:
Average number of dogs at an animal shelter: y = -3x + 42
Average number of cats at the animal shelter: y = 4x + 7
Where,
x = number of days after July 1
After how many days is the average number of cats and dogs at the shelter the same?
Equate both functions
-3x + 42 = 4x + 7
-3x - 4x = 7 - 42
-7x = -35
Divide both sides by -7
x = -35 / -7
= 5
x = 5 days
The correct answer is A. 5 days
The sum of the exterior and interior angles of a triangle is always 360°.
True or false.
A caterer is making cookie trays for upcoming holiday parties. This morning, she made 4 small trays and 4 large trays, which contain a total of 236 cookies. In the afternoon, she made 4 small trays and 1 large tray, which contain a total of 116 cookies. How many cookies do the different sized trays contain?
Answer:
The amount of cookies in the small tray = x = 19 cookies
The amount of cookies in the Large tray = y = 40 cookies
Step-by-step explanation:
Let
The amount of cookies in the small tray = x
The amount of cookies in the Large tray = y
We are told:
A caterer is making cookie trays for upcoming holiday parties.
This morning, she made 4 small trays and 4 large trays, which contain a total of 236 cookies.
This is represented Mathematically as:
4x + 4y = 236..... Equation 1
In the afternoon, she made 4 small trays and 1 large tray, which contain a total of 116 cookies.
This is represented Mathematically as:
4x + y = 116 ........ Equation 2
y = 116 - 4x
We solve the above equations using the substitution method
We substitute 116 - 4x for y in Equation 1
4x + 4y = 236..... Equation 1
4x + 4(116 - 4x) = 236
4x + 464 - 16x = 236
Collect like terms
4x - 16x = 236 - 464
-12x = -228
x = -228/-12
x = 19 cookies
Solving for y
y = 116 - 4x
y = 116 - 4 × 19
y = 116 - 76
x = 40 cookies
The number of cookies the different sized trays contained is given as:
The amount of cookies in the small tray = x = 19 cookies
The amount of cookies in the Large tray = y = 40 cookies
How can you verify trigonometric identities?
Answer:
Consequently, any trigonometric identity can be written in many ways. To verify the trigonometric identities, we usually start with the more complicated side of the equation and essentially rewrite the expression until it has been transformed into the same expression as the other side of the equation.
Step-by-step explanation:
simplify the complex fraction
Answer:
3.3333 (3 keeps repeating)
Step-by-step explanation:
Answer:
20/6 or 3 1/3
Step-by-step explanation:
4/3 / 2/5 can also be written as 4/3 x 5/2. That would equal 20/6, which when simplified equals 3 1/3
Without graphing, what are the vertex , axis of symmetry, and transformations of the parent function? Y - |8x-3| - 3
Given:
Consider the given function is
[tex]y=|8x-3|-3[/tex]
To find:
The vertex , axis of symmetry, and transformations of the parent function?
Solution:
We have,
[tex]y=|8x-3|-3[/tex]
[tex]y=\left|8\left(x-\dfrac{3}{8}\right)\right|-3[/tex]
[tex]y=8\left|x-\dfrac{3}{8}\right|-3[/tex] ...(i)
It is an absolute function.
The vertex form of an absolute function is
[tex]y=a|x-h|+k[/tex] ...(ii)
where, a is a constant, (h,k) is vertex and x=h is axis of symmetry.
From (i) and (ii), we get
[tex]a=8,h=\dfrac{3}{8},k=-3[/tex]
So,
[tex]\text{Vertex}:(h,k)=\left(\dfrac{3}{8},-3\right)[/tex]
[tex]\text{Axis of symmetry}:x=\dfrac{3}{8}[/tex]
Parent function of an absolute function is
[tex]y=|x|[/tex]
Since, a=8 therefore, parent function vertically stretched by factor 8.
[tex]h=\dfrac{3}{8}>0[/tex], so the function shifts [tex]\dfrac{3}{8}[/tex] unit right.
k=-3<0, so the function shifts 3 units down.
Therefore, the vertex is [tex]\left(\dfrac{3}{8},-3\right)[/tex] and Axis of symmetry is [tex]x=\dfrac{3}{8}[/tex]. The parent function vertically stretched by factor 8, shifts [tex]\dfrac{3}{8}[/tex] unit right and 3 units down.
Whitey needs to paint a block wall that is 75½ feet long. After
several hours he finished ¾ of it. How many feet does he still need to
paint?
Answer:
18.875 feet left, not sure if you need to round that or not
Answer:
18 7/8 feetStep-by-step explanation:
Total length of the wall to be painted = 75 1/2 feet
Already painted part = 3/4 of total length
Remaining part to be painted:
1 - 3/4 = 1/4 of total lengthRemaining part in feet:
75 1/2 * 1/4 = 151/2 * 1/4 =151/8 = 18 7/8 feet